Synching
Is there a way to recover photos from an iPhone you simply synced to iTunes and then restored without backing up? I switched from a 5 to a 6 and didn't realize I only synced.
iPhone 5s
I am guessing these photos were on Camera Roll on the iPhone 5. (Otherwise, they should be on your computer.)
So if you still have the iPhone 5, then back it up now and restore from it as instructed in the HT201269 article you attave ached above.
If you no longer have the iPhone 5 and the photos were on Camera Roll and not backed up, then they are gone.
UPDATE: If you used Photo Stream (related to iCloud) on the iPhone 5, they may show up in Photo Stream on the new iPhone.)